Show the Proof¶

In [1]:

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

Out[1]:

	step type	requirements	statement
0	instantiation	1, 2, 3, 4^*	, ⊢
	: , : , :
1	reference	20	⊢
2	instantiation	5, 6	, ⊢
	: , : , :
3	instantiation	7, 8	, ⊢
	: , :
4	instantiation	9, 51, 27, 26, 29, 28, 10, 35, 36	, ⊢
	: , : , : , : , : , :
5	axiom		⊢
	proveit.logic.equality.substitution
6	modus ponens	11, 12	, ⊢
7	theorem		⊢
	proveit.logic.equality.equals_reversal
8	instantiation	13, 28, 31	, ⊢
	: , :
9	theorem		⊢
	proveit.numbers.multiplication.disassociation
10	modus ponens	14, 18	⊢
11	instantiation	15, 24	⊢
	: , : , : , : , : , : , :
12	generalization	16	, ⊢
13	modus ponens	17, 18	⊢
14	instantiation	19	⊢
	: , : , :
15	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
16	instantiation	20, 21, 22	, , ⊢
	: , : , :
17	instantiation	23, 26, 24, 51	⊢
	: , : , : , : , : , :
18	generalization	32	⊢
19	theorem		⊢
	proveit.numbers.summation.summation_complex_closure
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	25, 26, 27, 51, 28, 29, 35, 36, 32	, , ⊢
	: , : , : , : , : , :
22	instantiation	30, 31, 32	, , ⊢
	: , :
23	theorem		⊢
	proveit.numbers.multiplication.distribute_through_summation
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
25	theorem		⊢
	proveit.numbers.multiplication.association
26	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
28	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
29	instantiation	33	⊢
	: , :
30	theorem		⊢
	proveit.numbers.multiplication.commutation
31	instantiation	34, 35, 36	, ⊢
	: , :
32	instantiation	37, 38, 39	⊢
	: , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
35	assumption		⊢
36	assumption		⊢
37	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
38	instantiation	49, 41, 40	⊢
	: , : , :
39	instantiation	49, 41, 42	⊢
	: , : , :
40	instantiation	49, 44, 43	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	instantiation	49, 44, 45	⊢
	: , : , :
43	instantiation	49, 47, 46	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	49, 47, 48	⊢
	: , : , :
46	assumption		⊢
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
48	instantiation	49, 50, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements